Features of stochastic decay in the magnetoactive plasma
The regular and stochastic decay processes of transverse electromagnetic waves in the magnetoactive plasma investigated. The essential attention noted to decay into oscillations with dynamics that takes into account ion plasma component. The threshold of transition into dynamics chaos defined. It w...
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| Cite this: | Features of stochastic decay in the magnetoactive plasma / V.A. Buts, I.K. Kovalchuk // Вопросы атомной науки и техники. — 2018. — № 4. — С. 208-212. — Бібліогр.: 15 назв. — англ. |
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Buts, V.A. Kovalchuk, I.K. 2019-02-14T18:41:41Z 2019-02-14T18:41:41Z 2018 Features of stochastic decay in the magnetoactive plasma / V.A. Buts, I.K. Kovalchuk // Вопросы атомной науки и техники. — 2018. — № 4. — С. 208-212. — Бібліогр.: 15 назв. — англ. 1562-6016 PACS: 52.35.Mw https://nasplib.isofts.kiev.ua/handle/123456789/147439 The regular and stochastic decay processes of transverse electromagnetic waves in the magnetoactive plasma investigated. The essential attention noted to decay into oscillations with dynamics that takes into account ion plasma component. The threshold of transition into dynamics chaos defined. It was shown that transition may take place at abnormally small amplitudes of decaying wave. Dynamics of fields in the dynamics chaos regime investigated. Досліджені регулярний і стохастичний процеси розпаду поперечної електромагнітної хвилі в магнітоактивній плазмі. Особлива увага приділена розпаду на низькочастотні коливання за участю динаміки іонної компоненти плазми. Визначений поріг переходу в режим динамічного хаосу. Показано, що він може відбуватися при аномально малих амплітудах хвилі, що розпадається. Досліджена динаміка полів у режимі динамічного хаосу. Исследованы регулярный и стохастический процессы распада поперечной электромагнитной волны в магнитоактивной плазме. Особое внимание уделено распаду на низкочастотные колебания с участием динамики ионной компоненты плазмы. Определен порог перехода в режим динамического хаоса. Показано, что он может происходить при аномально малых амплитудах распадающейся волны. Исследована динамика полей в режиме динамического хаоса. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Нелинейные процессы Features of stochastic decay in the magnetoactive plasma Особливості стохастичного розпаду в магнітоактивній плазмі Особенности стохастического распада в магнитоактивной плазме Article published earlier |
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| title |
Features of stochastic decay in the magnetoactive plasma |
| spellingShingle |
Features of stochastic decay in the magnetoactive plasma Buts, V.A. Kovalchuk, I.K. Нелинейные процессы |
| title_short |
Features of stochastic decay in the magnetoactive plasma |
| title_full |
Features of stochastic decay in the magnetoactive plasma |
| title_fullStr |
Features of stochastic decay in the magnetoactive plasma |
| title_full_unstemmed |
Features of stochastic decay in the magnetoactive plasma |
| title_sort |
features of stochastic decay in the magnetoactive plasma |
| author |
Buts, V.A. Kovalchuk, I.K. |
| author_facet |
Buts, V.A. Kovalchuk, I.K. |
| topic |
Нелинейные процессы |
| topic_facet |
Нелинейные процессы |
| publishDate |
2018 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Особливості стохастичного розпаду в магнітоактивній плазмі Особенности стохастического распада в магнитоактивной плазме |
| description |
The regular and stochastic decay processes of transverse electromagnetic waves in the magnetoactive plasma investigated. The essential attention noted to decay into oscillations with dynamics that takes into account ion plasma
component. The threshold of transition into dynamics chaos defined. It was shown that transition may take place at
abnormally small amplitudes of decaying wave. Dynamics of fields in the dynamics chaos regime investigated.
Досліджені регулярний і стохастичний процеси розпаду поперечної електромагнітної хвилі в магнітоактивній плазмі. Особлива увага приділена розпаду на низькочастотні коливання за участю динаміки іонної
компоненти плазми. Визначений поріг переходу в режим динамічного хаосу. Показано, що він може відбуватися при аномально малих амплітудах хвилі, що розпадається. Досліджена динаміка полів у режимі динамічного хаосу.
Исследованы регулярный и стохастический процессы распада поперечной электромагнитной волны в
магнитоактивной плазме. Особое внимание уделено распаду на низкочастотные колебания с участием динамики ионной компоненты плазмы. Определен порог перехода в режим динамического хаоса. Показано, что
он может происходить при аномально малых амплитудах распадающейся волны. Исследована динамика
полей в режиме динамического хаоса.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147439 |
| citation_txt |
Features of stochastic decay in the magnetoactive plasma / V.A. Buts, I.K. Kovalchuk // Вопросы атомной науки и техники. — 2018. — № 4. — С. 208-212. — Бібліогр.: 15 назв. — англ. |
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AT butsva featuresofstochasticdecayinthemagnetoactiveplasma AT kovalchukik featuresofstochasticdecayinthemagnetoactiveplasma AT butsva osoblivostístohastičnogorozpaduvmagnítoaktivníiplazmí AT kovalchukik osoblivostístohastičnogorozpaduvmagnítoaktivníiplazmí AT butsva osobennostistohastičeskogoraspadavmagnitoaktivnoiplazme AT kovalchukik osobennostistohastičeskogoraspadavmagnitoaktivnoiplazme |
| first_indexed |
2025-11-24T06:31:16Z |
| last_indexed |
2025-11-24T06:31:16Z |
| _version_ |
1850843064057200640 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2018. №4(116) 208
NONLINEAR PROCESSES
FEATURES OF STOCHASTIC DECAY
IN THE MAGNETOACTIVE PLASMA
V.A. Buts1,2,3, I.K. Kovalchuk1
1National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine;
2Institute of Radio Astronomy of NAS of Ukraine, Kharkov, Ukraine;
3V.N. Karazin Kharkiv National University, Kharkov, Ukraine
E-mail: vbuts@kipt.kharkov.ua, kovalchuk-ik@rambler.ru
The regular and stochastic decay processes of transverse electromagnetic waves in the magnetoactive plasma in-
vestigated. The essential attention noted to decay into oscillations with dynamics that takes into account ion plasma
component. The threshold of transition into dynamics chaos defined. It was shown that transition may take place at
abnormally small amplitudes of decaying wave. Dynamics of fields in the dynamics chaos regime investigated.
PACS: 52.35.Mw
INTRODUCTION
Wave interaction is one of the fundamental process-
es in the plasma physics and plasma electronics. The
linear processes of such interaction well investigated.
The weakly nonlinear interactions are enough well in-
vestigated essentially three wave interaction in isotropic
plasma are investigate in detail (see [1 - 3]). In particu-
lar, in the work [1], in general the algorithm that allows
to obtain equations describing not only wave interaction
in isotropic matter but in gyrotropic one too was formu-
lated. But, it is needed to note that dynamics in gyro-
tropic matters practically was not studied. It is condi-
tioned, first of all that this studying has large technical
difficulties. These difficulties is conditioned first of all
by abundant dispersion properties of gyrotropic matters
(magnetoactive plasma). In connection with these diffi-
culties the issue about three wave interaction in gyro-
tropic plasma was only slightly affected in [4]. It needed
to note also one feature of work where three wave pro-
cesses in plasma consider. This connected with that
practically in all works the dynamics of electron com-
ponent of plasma only considered
In presented work the process of three wave interac-
tion magnetoactive plasma is considering. In this case as
ordinary decay as modified one will considered. The
modified decay is such process where linear stage is
characterized by increment that is large than frequency
of low frequency wave taking part in the process of
three wave interaction. Below in the section 2 the equa-
tions describing three wave interaction with taking into
account low frequency oscillations properties of that in
particular defined by ion component of plasma. In this
section, the analytical expression for criterion of transi-
tion of regular dynamics into stochastic decay regime
obtained. In the third section the process of stochastic
dynamic of interacting wave considered. In conclusion
the main results formulated.
1. FORMULATION OF PROBLEM
AND BASIC EQUATIONS
Nonlinear wave interaction in plasma well studied
area of plasma physics. Usually studying of processes of
such wave interaction is limited by weakly nonlinear
approximation. In this approach, it is supposed that in
the interaction the natural waves of electrodynamics
system take part. Amplitudes of these waves slowly
vary in time and space under influence of nonlinear pro-
cess. The simplest case when three waves take part in
interaction studied most in detail. The basic approaches
and results in this area presented, for example, in works
[1 - 3]. In the work [5, 6] it was shown that three wave
decay processes may be chaotic. The criterion of trans-
fer to chaos has been found in this work. Some aspects
of the dynamic of chaotic decays considered in [7 - 12].
The results of numerical investigation presented in these
work, the spectrum and correlation functions presented
too. It was shown if transition of decay into chaotic re-
gime takes place, spectrum of interacting waves is ex-
panding. Width of correlation function is finite. The
results of analytical and numerical investigations have
been confirmed by experiment.
In this work the process of three wave decay in un-
limited gyrotropic matter (magnetoactive plasma) will
be investigated. It is supposed that external uniform
magnetic field is directed along z axis and interacting
waves may propagate under arbitrary angle relatively
magnetic field direction. The space and temporal de-
pendence of electromagnetic field may be presented as
sum eigen waves and has next form
( , ) ( , ) exp( )m m m
m
E r t E r t i t ik rω= −∑
, (1)
where ( , )mE r t
– complex slowly varying amplitude of
wave, mω and mk
– are frequency and wave vector cor-
respondingly. Algorithm for obtaining equations for
slowly varying amplitudes of waves taking part in decay
process in the infinitely extended uniform plasma pre-
sented in works [1 - 3] in detail. In [1] it generalized for
magnetoactive plasma. Nonlinear dispersion equation
for one of the interacting wave has the following form:
( )
( )
222 *
2
*
2
4 ,
m
m m m m
m nl m
k e k e e E
c
i e j
c
α αβ β
ω
e
πω
− − =
=
(2)
where mE – module of complex of amplitude of wave
taking part in decay process, /m m me E E=
– unit wave
vector of polarization, αβe – permittivity tensor of
mailto:vbuts@kipt.kharkov.ua
mailto:kovalchuk-ik@rambler.ru
ISSN 1562-6016. ВАНТ. 2018. №4(116) 209
magnetoactive plasma, c – velocity of light, ( )nl m
j
–
nonlinear current. Expressions for components of per-
mittivity tensor for magnetoactive plasma may be find
in [13, 14].
In the nonlinear addendums (items, summands) tak-
ing into consideration multiplication of perturbation of
density and velocity plasma waves taking part in decay
process. The multiplication of perturbation of density
and velocity of the plasma waves taking part in decay
process has been taken into consideration in the nonlin-
ear items. In this case perturbations corresponding linear
approximation are used. In order to right part of equa-
tion (2) was resonant to the left part the frequencies and
wave vectors must satisfy to synchronism conditions
1 2 3 1 2 3, ,k k kω ω ω= + = +
(3)
where 1ω , 1k
– frequency and wave vector of decaying
waves, 2ω , 3ω – frequencies of waves arising in the
decay, 2k
, 3k
– their wave vectors.
Equation (2) for decaying wave may be presented in
the form:
( )*
1 12 1
4( , ) nlD k E i e j
c
πωω =
. (4)
Here ( )
222 *
2( , )D k k ek e e
c α αβ β
ωω e= − −
. As a re-
sult of nonlinear interaction amplitudes of wave slowly
vary. So modes taking part in decay process is not mon-
ochromatic. They are wave packets with some spreading
on frequencies and wave vectors. So expression for dis-
persion equation may be decomposed into Taylor series
on small variations on frequency and wave vector from
values that are dispersion of monochrome linear disper-
sion equation. Function ( , )D kω
may be presented in
the form
( ) ( )1 1 1 1
1 1 1 1
( , ) ( , )
( , ) ( , )
D k D kD k D k k k
k
ω ω
ω ω ω ω
ω
∂ ∂
= + − + −
∂ ∂
. (5)
Wave with parameters ( )1 1,kω
is eigen modes for
considering electrodynamic system, so the next condi-
tion is satisfies:
1 1( , ) 0D kω =
. (6)
To transfer to space and temporal variables it is
needed to perform. The inverse Fourier transformation
is needed to use to the nonlinear dispersion equation for
transfer to space and time variables. This procedure
described in detail in [1, 3]. As a result taking into ac-
count condition (6) differential equation in partial deriv-
atives for slowly varying amplitudes of interacting
waves are obtained. Below equation for decaying wave
is presented:
( ) ( )
( )
*
11 1 1 1
1 1 2
1 1 1
4
,
,
nl
gr
e jE Ev k i
t r c A k
πω
ω
ω
∂ ∂
+ =
∂ ∂
, (7)
where ( )1 1,grv kω
– group velocity of this wave,
( ) ( ),
,
i i
i i i
D k
A k
ω
ω
ω
∂
=
∂
. Index j points to any interact-
ing waves.
The perturbations of density and velocity of plasma
electrons and ions, containing in nonlinear current, can
be expressed through slowly varying amplitudes of
waves, taking part in nonlinear interaction. These ex-
pressions may be obtained from linear approach of hy-
drodynamics equations. Analogous equations may be
obtained for slowly varying amplitudes that waves
which be excited in the decay process. As result, analyt-
ical expressions for right parts of equations describing
nonlinear wave interaction of three waves may be ob-
tained. These expressions are lengthy, so do not present
here.
In the compact form equations describing nonlinear
interaction in particular wave decay may be presented in
next form:
1
2 3
*2
1 3
2
2 *3
3 3 1 22
,
,
,
a Va a
t
a Va a
t
a a Va a
t
ω
∂
=
∂
∂
= −
∂
∂
+ = −
∂
(8)
where V – matrix elements of interaction. The change
of variables describing electromagnetic field presented
in [1] and using of conservation laws for energy and
momentum allows to transform set (8) to form where
matrix elements of interaction containing in different
equations are equal. In the equation (8) there was taken
into account that third low frequency wave itself may
slowly vary. So we conserve it oscillation properties. If
amplitude of decaying wave is enough small that incre-
ment of decay instability is less than frequency of LF
wave the third equation of set (8) may be done short-
ened. It has form:
*3
1 2
a
Va a
t
∂
= −
∂
. (9)
In this case set of equations (8) coincides with one
that presented by many others (see, for example [1 - 3)].
It is possible to use results obtained in these works. The
existing in this set integrals, named Manly-Row correla-
tion, are most impotent for us:
2 2
1 2
2 2
1 3
,
.
a a const
a a const
+ =
+ =
(10)
There are also two integrals:
2 2 2
1 1 2 2 3 3
1 2 3
,
sin ,
a a a const
a a a const
ω ω ωΣ = + + =
Φ =
. (11)
where Σ – total energy of interacting waves,
1 2 3 1 2 3, , ,ϕ ϕ ϕ ϕ ϕ ϕΦ = − − – phases of slowly varying
complex amplitudes 1 2 3, ,a a a ( )( )expj j ja a iϕ= .
Solution of set (8) taking into account equation (9) in-
vestigated in [2]. The qualitative analysis presented in
[1]. Decay dynamics is periodical exchange by energy
between interacting modes.
Coming back to set of equations (8) it is possible to
define criterion for onset of regime with dynamics cha-
os. This regime arises when amplitude of decaying
wave will be enough large that increment of decay in-
stability will be larger than frequency of LF wave. Such
ISSN 1562-6016. ВАНТ. 2018. №4(116) 210
estimation obtained in work [5, 6]. We may use this
estimation:
( )2 3
10
min ,
a
V
ω ω
> , (12)
where 10a – initial amplitudes of decaying wave. As it
seen from expression (12) this phenomenon have
threshold character.
2. ANALYTICAL EXPRESSION CRITERION
OF ARISING OF STOCHASTIC
INSTABILITY
Expression (12) is general. It does not contain pa-
rameters of the waves taking part in interaction. Earlier
expression (12) was concretized for case of waves that
characteristic was defined by electron component of
plasma only. Below we will consider case of interaction
of wave property of which defined not only by electron
components, but ion one too.
Further we will consider such decay when frequen-
cies of wave nonlinearly interacting satisfy following
relations:
1 2 3 1 2 3, .k k kω ω ω≈ >> ≈ ≈ (13)
As 1ω and 2ω in magnetoactive plasma it can be HF
electromagnetic waves, which frequencies are very
close. In works [7 - 12] the case is considered when
lowest frequency was defined by electron component
dynamics and its frequency was order Langmuir one. In
this work we interest by decay in which dispersion
properties of low frequency significantly defined by ion
component of the plasma. In particular, it may be
Alfven wave. In this case it's frequency is close to ion
cyclotron frequency. One can expect that in this case
threshold of transfer to stochasticity will be more less
than in case Langmuir waves. The waves with low fre-
quency that are excited in such decay may be used for
heating of ion plasma. Thus we have physical mecha-
nism, allowing excites LF waves in plasma. These
waves can be used for heating plasma ions.
Let's get an analytical expression for the criterion of
transition to chaotic dynamics. For this we use equation
(7) that after simplification may be presented in such
form:
*
1 11 1
2
1
4 nle jE
t Ac
πω∂
= −
∂
. (14)
Expression for current density containing in right
part of equation (13) may be presented as following:
( ) ( )(1)
1 2 3 3 2nl e e e ej e n v e n v= − −
. (15)
Expression for perturbation of electron density is:
0 3
3 32
3
z
e z
e
n ek
n i E
m ω
= − . (16)
From this follows:
0 3 2
3 2 3 2 2 32 2
23 3
1z z
e e z z
ee
n ek een v E E E E
mm ωω ω
= − ≈ . (17)
Using these expressions the (14) may be presented
in the following form:
1
2 3
E VE E
t
∂
=
∂
. (18)
From these the expression for matrix element fol-
lows:
2
3
2 2
1 3
1pe
e
ek
V
m c A
ω
ω
= . (19)
It is needed to note that value of this element is in-
versely proportional to square of low frequency. This
means that width of nonlinear resonance becomes the
large the lower is frequency of LF wave. About nonlin-
ear resonance see work [5, 6]. Thus in our case not only
distance between nonlinear resonances decreases (this
distance decreases proportional to first power of fre-
quency of LF wave) but width of nonlinear resonance
increase.(inversely proportional to square frequency of
LF wave). As a result value of strength of decaying HF
wave that is needed for appearance of regime with dy-
namics chaos will be proportional to third power the
frequency of LF wave:
2
3 1
3 2
3
e
th
pe
m c A
E
ek
ω
ω
= , (20)
where em – mass of electron, peω – electron plasma
frequency. From (20) it follows that strength of HF
wave which is needed for appearance of stochastic de-
cay will be abnormally small for decay with participa-
tion of waves which properties defined by ions of plas-
ma.
3. DYNAMICS OF WAVES
IN THE STOCHASTIC REGIME
In the overwhelming majority of cases wave dynam-
ics in the stochastic regime is fact that main sensitive
and easily varying parameters of the interacting waves
are their phases. Additional argument for such affirma-
tion is well known fact that amplitudes of interacting
waves may be considered in many cases as adiabatic
invariants. Besides, if do not concretize reason of ap-
pearance of chaotic regime in many cases analysis of
chaotic regimes occurses namely with accounting of
this fact. In particular, such analysis was used in work
[2]. Below we will follow to this analyses algorithm.
The set of equations (8) describes three wave decay
in that case when waves participating in nonlinear inter-
action are regular. In the opposite case nonlinear inter-
action is becoming stochastic. This process is describing
by equations of decay process with random phases.
Their obtaining described in detail in [1, 3]. After transi-
tion of regular decay process into stochastic regime it
dynamics may be described by equations with random
phases. We use algorithm described in [1]. First of all
we note that set of equations (8) may be presented in
next way
( )
( )
( )
2
1 * * *
1 2 3 1 2 3
2
2 * * *
1 2 3 1 2 3
2
3 * * *
1 2 3 1 2 3
,
,
.
a
V a a a a a a
t
a
V a a a a a a
t
a
V a a a a a a
t
∂
= +
∂
∂
= − +
∂
∂
= − +
∂
(21)
After complex transformations set of equations for
modules of slowly varying complex wave amplitudes
with random phases will have form:
ISSN 1562-6016. ВАНТ. 2018. №4(116) 211
( )1
2 3 1 2 1 3
32 1
,
,
N W N N N N N N
t
NN N
t t t
∂
= − −
∂
∂∂ ∂
= = −
∂ ∂ ∂
(22)
where 2
i iN a= , 2W V τ= , τ – correlation time be-
tween phases.. This set of equations as (8) has integrals
(10). Manly-Row correlations allow to transform set of
equations (22) to one ordinary differential equation of
first order:
( )2 12 131
1 12 13 1
23
3 3
C CN W N C C N
t
∂ = − + + ∂
, (23)
or
( )( )(1) (2)1
1 1 1 13
N W N N N N
t
∂
= − −
∂
, (23a)
where 12 10 20C N N= + , 13 10 30C N N= + , 10 20 30, ,N N N
– initial values of 1 2 3, ,N N N correspondingly,
( )(1,2) 2 2
1 12 13 12 12 13 13
1 1
3 3
N C C C C C C= + ± − + .
Unlike from (8) equation (23) has stationary points
that equal to (1)
1N and (2)
1N . Analytical analysis shows
that first of them is unstable and second is stable. It may
show when time tends to infinity solution tends to stable
stationary point independent from initial conditions.
Expressions for values of stationary point of 2 3,N N do
not present here because they are enough complex. Sta-
tionary values for 1 2 3, ,N N N when conditions
10 20 30,N N N>> are satisfied have the form:
( )
( )
( )
(2)
1 10 20 30
(2)
2 10 20 30
(2)
3 10 20 30
1 2 ,
6
1 4 5 ,
6
1 4 5 .
6
N N N N
N N N N
N N N N
= + +
= + −
= − +
. (24)
As it seen from expressions (24) in the stochastic re-
gime of three wave decay when the amplitude of decay-
ing wave is significantly large than amplitudes of other
waves on large temporal interval the square of first
wave module will have one third part of it initial value.
Squares of modules of waves that generated in decay
process essentially increase and will have two third
parts from square of initial amplitude value of first
wave. But almost all energy will be contained in the
first and second waves (because energy of each wave is
proportional it frequency 2
i i iaωΣ = )).
CONCLUSIONS
Note the most important results of presented analy-
sis. First of all note attention that threshold of appear-
ance of regimes with dynamics chaos at three wave in-
teraction abnormally fast decreases when frequency of
LF wave participating in interaction decreases. In par-
ticular, this means that practically at any strength of
transverse wave that propagates in plasma there are re-
gimes with dynamics chaos at participation of LF wave
that properties are defined by ion component of plasma.
But it is needed to note that such regime may not be
immediately detected from characteristics of transverse
LF waves. The thing is the smaller amplitude of the HF
wave, the smaller diffusion coefficient that characterizes
spreading characteristics (first of all of frequency) HF
wave. This dynamics (chaotic) may be most significant
for ion component of plasma. Plasma ions may enough
effectively heat. But note that with increasing ampli-
tudes of decaying wave electron component of plasma
may participate in stochastic dynamics. In this case this
component (electron) may take main energy stream of
decaying wave. In this case the heating of ion compo-
nent of plasma may decrease.
The stochastic regime of decay analyzed. The stable
stationary point is defined. It was shown when square of
module of initial amplitude of decaying wave essential-
ly exceeds analogous value of others waves in the stable
stationary point the first wave has only third part from
initial value. Square of amplitude modules of two others
wave are increasing to two third parts of this value of
first wave.
Note that above one stage of regular and chaotic
three wave decay considered. Such stages may be much.
High frequency wave appeared as result of first stage
may decay into other more low frequency transverse
wave and low frequency one. Such stages may organize
cascade of enough number elementary stages. The dy-
namics of such decays significantly were studied in
work [7, 15]. In this case much larger part of energy
may be transferred into low frequency region when exist
only one stage of decay. It needed to note that above
only one low frequency branch of oscillation was take
into consideration. In real experiments may participate
other branches. The theory of such decays is complex.
But it may expect that in these cases namely low fre-
quency region of wave spectrum will be saturated by
significant amount of energy. Such mechanism of ener-
gy transfer of regular high frequency wave into region
of low frequency wave with stochastic dynamics appar-
ently may be effectively used for heating of plasma ion
component.
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http://arxiv.org/abc/1210.6788.
Article received 01.06.2018
ОСОБЕННОСТИ СТОХАСТИЧЕСКОГО РАСПАДА В МАГНИТОАКТИВНОЙ ПЛАЗМЕ
В.А. Буц, И.К. Ковальчук
Исследованы регулярный и стохастический процессы распада поперечной электромагнитной волны в
магнитоактивной плазме. Особое внимание уделено распаду на низкочастотные колебания с участием дина-
мики ионной компоненты плазмы. Определен порог перехода в режим динамического хаоса. Показано, что
он может происходить при аномально малых амплитудах распадающейся волны. Исследована динамика
полей в режиме динамического хаоса.
ОСОБЛИВОСТІ СТОХАСТИЧНОГО РОЗПАДУ В МАГНІТОАКТИВНІЙ ПЛАЗМІ
В.О. Буц, І.К. Ковальчук
Досліджені регулярний і стохастичний процеси розпаду поперечної електромагнітної хвилі в магнітоак-
тивній плазмі. Особлива увага приділена розпаду на низькочастотні коливання за участю динаміки іонної
компоненти плазми. Визначений поріг переходу в режим динамічного хаосу. Показано, що він може відбу-
ватися при аномально малих амплітудах хвилі, що розпадається. Досліджена динаміка полів у режимі дина-
мічного хаосу.
http://arxiv.org/abc/1210.6788
INTRODUCTION
1. FORMULATION OF PROBLEM AND BASIC EQUATIONS
2. ANALYTICAL EXPRESSION CRITERION OF ARISING OF STOCHASTIC INSTABILITY
3. DYNAMICS OF WAVES IN THE STOCHASTIC REGIME
CONCLUSIONS
references
ОСОБЕННОСТИ СТОХАСТИЧЕСКОГО РАСПАДА В МАГНИТОАКТИВНОЙ ПЛАЗМЕ
ОСОБЛИВОСТІ СТОХАСТИЧНОГО РОЗПАДУ В МАГНІТОАКТИВНІЙ ПЛАЗМІ
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